Last visit was: 12 Jul 2024, 19:43 It is currently 12 Jul 2024, 19:43
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Intern
Intern
Joined: 28 Feb 2012
Posts: 20
Own Kudos [?]: 253 [21]
Given Kudos: 1
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94302
Own Kudos [?]: 640183 [8]
Given Kudos: 84576
Send PM
User avatar
Manager
Manager
Joined: 24 Jul 2011
Posts: 57
Own Kudos [?]: 422 [5]
Given Kudos: 5
Location: India
Concentration: Strategy, General Management
GMAT 1: 670 Q49 V33
WE:Asset Management (Manufacturing)
Send PM
General Discussion
Senior Manager
Senior Manager
Joined: 24 Aug 2009
Posts: 388
Own Kudos [?]: 2292 [0]
Given Kudos: 276
Concentration: Finance
Schools:Harvard, Columbia, Stern, Booth, LSB,
Send PM
Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Bunuel wrote:
sandal85 wrote:
You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 centimeters. The number of non-congruent triangles that can be formed by choosing three of the sticks to make the sides is

A. 3
B. 6
C. 7
D. 10
E. 12

OA will be posted after some time.

Please inclease my Kudos if you like the problem...


The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

Based on this there can be only 7 triangles formed: (20, 30, 40), (20, 40, 50), (20, 50, 60), (30, 40, 50), (30, 40, 60), (30, 50, 60), (40, 50, 60).

Answer; C.


Hi Bunuel,

Is there any other method (combinatorics) to solve this question ?
User avatar
Manager
Manager
Joined: 02 Nov 2014
Posts: 146
Own Kudos [?]: 436 [0]
Given Kudos: 75
GMAT Date: 08-04-2015
Send PM
Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Got this correct :-D but spent 3.48 :(
Used trial and error, keeping the basic properties of triangle in mind.

Anybody has a better / faster method??

Thanks.
VP
VP
Joined: 10 Jul 2019
Posts: 1385
Own Kudos [?]: 576 [0]
Given Kudos: 1656
Send PM
You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
1st, you can not form a valid triangle with any other 2 sides if 1 of the Sides picked =10. The Triangle will always fail the Triangle Test for Validity (the 2 Smaller Side Lengths will NEVER be greater than > Longest Side Length)

The 7 Triangles that will work after using the TEST: 2 Shorter Side Lengths > 3rd Longest Side Length


20 - 30 - 40

20 - 40 - 50

20 - 50 - 60

30 - 40 - 50

30 - 40 - 60

30 - 50 - 60

40 - 50 - 60


Since there are only "5 Choose 3" = 20 Different Combinations of 3 Sticks Picked, if you can quickly realize that 10 can never be a valid Side for Any Triangle formed with any of the 2 other sides given, you can cut that down to 10 Triangle Values that you need to Test.

Moving quickly, it's possible to get it finished within 2 - 3 minutes.

EDIT: I said it's "possible. I didn't say I was able to do it lol.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33953
Own Kudos [?]: 851 [0]
Given Kudos: 0
Send PM
Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Moderator:
Math Expert
94302 posts